The Keep (address and info)
The underground cocktail bar that is literally underground, and not "underground" in the sense of being under-the-radar, offers classic cocktails for $5-9 and $2 High Lifes Monday through Friday from 4-7pm.
Republic (address and info)
Grand River Ave
On Tuesdays through Fridays from 4-6pm, get select cocktails (Old Fashioned, gimlet, Collins) for $5, wine for $5, a rotating bottled beer selection for $3-5, and pours for $4 (including Old Forrester, SCORE), and select snacky plates for $3-8.
Dime Store (address and info)
This is the kind of happy hour that involves more advanced math than most people are probably capable of once they get real deep into the happy hour itself, but it goes like this: on Tuesday through Friday from 3-6pm, you'll get 50% off alcohol from 3-4pm, 40% off alcohol for 4-5pm, and 30% off alcohol from 5-6pm. This is the law of diminishing returns of happy hours, so get there early to get the most value.
Downtown Louie's Lounge (address and info)
Grand Circus Park
Monday through Friday from 3-6pm, get $2 domestic bottled beer (excludes craft beers, boooo), $2 Bud Light pints, and $3 tallboys. There are also $5 wines & well pours, and $2 off all appetizers.
Roast (address and info)
Perhaps you've heard that Roast's happy hour was once the most famous happy hour in Detroit? And that's still more or less true. Happy hour is Monday through Friday from 4-6:30pm: select wines & beers are $4, well drinks are $5. Plus, starting at 4:30pm, you get half off everything on the bar menu, which includes the famous Roast Burger, and the less famous, but equally delicious, chicken livers & creamy polenta. (Happy hour is only available in the bar.)
Cliff Bell's (address and info)
More math to confuse you with. Ready? OK: Tuesdays through Fridays from 4-7pm, get $3 drafts and wells drinks, half-off craft cocktails, $5 select wines, and cheap PBR that starts at 50 cents at 4pm and gets more expensive as the night progresses (but is still cheap, because it's PBR). There's also a small shareable plates happy hour menu, with most items $5-6.
Grand Trunk Pub (address and info)
Campus Martius Park
(Foran's) Grand Trunk Pub doesn't so much do a "happy hour" as a bunch of regular weekly specials, the best of which is $3 draft Tuesdays from 6-8pm. (Keep in mind that all the drafts are craft.) It also pays to treat a Monday like a Friday, when happiest hour from 11pm-1am gets you $1 off drafts, $2 well drinks, $2 domestic macros, and probably some shot specials. Sunday is industry night, with $2.50 first drafts, plus $1 shots to go with that first draft, and $3 shots of Tullamore Dew.
Coach Insignia (address and info)
West Jefferson Ave/Renaissance Center
From the highest bar perch in the city, enjoy happy hour from 4-7pm Monday through Friday with a special menu and different deals daily. There are $4 select bottles and $5 personal pizzas on Mondays, half off Michigan beer and wine on Tuesdays, $4 select bottles & $5 burgers on Wednesdays, half off signature cocktails on Thursdays, and reverse happy hour that runs 9pm-close on Fridays.
London Chop House (address and info)
LCH too expensive for you? Then stop in Monday through Friday from 3:30-6:30pm for $6 martinis & Manhattans, select wines poured at $1 apiece, local drafts half off, and $2 Stroh's bottles, and a special food menu, with prices that range $5-13 for small tastes of the larger menu, including 3oz filet mignon medallions, escargot, and a $5 U-12 shrimp cocktail.
Firebird Tavern (address and info)
Hey guys, it's baseball season once again! Which probably means you'll be hanging out a lot more in Greektown. Which means you should take advantage of the happy hour at Firebird Tavern: half off all American craft beers & wine from 4:30-6:30pm Monday through Friday.